DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.25888#0044
28
ENGINEER AND MACHINIST’S DRAWING-BOOK.
pose, the triangle of 60° is preferable to that of 45°, as it
is longer and lighter.
When the parallels and perpendiculars do not coincide
in direction with the edges of the board, the square may
be adjusted with its bevel stock to the obliquity required,
and the lines may be drawn as before. This is probably
the best plan when the oblique lines are numerous or
extensive. In most cases, however, oblique lines are only
occasional, and when their position is given they may be
drawn with a straight-edge. When the oblique parallels
and perpendiculars are short, as in oblique framing, short
rods, or bars, bolt-heads, and the like, the combined use of
the straight-edge and triangle is expedient. Thus, to draw
a perpendicular to the oblique line A B (Fig. 118), at the
point C, set the straight-
edge and set-square in
conjunction, to bring
the long edge of the
square to coincide with
the given line at a b;
then shift the square
into the position show-
ing in dotting, while the straight-edge is held fast,
and draw the perpendicular. When a number of short
parallels are to be drawn to an oblique line A B (Fig. 119),
through given points C, D, E, set the triangle and
straight-edge as before, with the side a b coincident with
the given line; then slide the triangle into the positions
shown in dotting, to set the edge upon the given points,
and draw the parallels as required. The straight-edge, in
these cases, is oblique to the given line, and may in some
cases be inconveniently placed, requiring re-adjustment,
when a number of lines are to be drawn. It is thus some-
times convenient to employ a supplementary triangle ; in
the second case, for example, the triangle might be set to
the given line, slid down to the position E, and fixed
there ; and a second triangle placed on its edge E, which
would form a sliding surface parallel to the given line,
from which perpendiculars might be drawn. Or, the tri-
angle a b c (Fig. 120) may be placed with its edge a c to
coincide with the given line, and the straight-edge applied
to the side b c; sliding the triangle into the position a' b' c,
the edge a'd now forms a base-line parallel to the given
line from which perpendiculars may be drawn with a
second triangle d.
Parallel rulers are also frequently used for drawing
oblique lines. We have no great opinion of them, except
for sketching jobs, as they are at best inconvenient for
working, and liable to derangement at the joints.
It remains to consider the utility of the sector in draw-
ing oblique parallel lines. This instrument should be stiff
enough at the joint not to yield too readily; and by set-
ting it to the obliquity required, it may be slid along the
square-blade, and may thus command the entire range of
the board. By sliding the triangle upon the sector, oblique
perpendiculars may also be drawn, as in (Fig. 118).
Frequently, short oblique lines, perpendicular to each
other, require to be drawn at the same place; this may
occasionally be done in one setting of the sector or straight-
edge, by placing the slant side of the triangle next it, and
exposing the right angle.
Thus, in drawing a
square nut n (Fig. 121), it
is plain from the figure,
that by presenting the
two edges of the tri-
angle successively, all
the sides of the nut may be drawn.
Square figures may be quickly described with the use
of the board. If they are to be described on a given
centre, C (Fig. 122), describe a circle with the radius C D
equal to half the side of the square, draw parallels A B,
E F, with the square, touching the top and bottom of the
circle, which may be very correctly drawn as tangents by
the eye, and with the set-square draw the upright tan-
gents, in the manner shown in dotting, to complete the
figure.
(.Fig. 122.) (Fig. 123.)
If the square is to be drawn upon a given line A B
(Fig. 123), draw the diagonal lines A F, BE, from the ends
of the line, by means of the set-square of 45°, as exempli-
fied in the figure, and draw perpendiculars from the same
points, cutting the diagonals at E, F ; join E F to com-
plete the figure.
To draw an octagon, apply the set-square of 45° to the
corners, after completing a square figure, and draw tan-
gents to the inscribed circle, as, for example, the line h k,
(Fig. 114).
To draw an equilateral triangle upon a given line A B
(Fig. 124), it is only necessary to apply the slant edge of the
set-square of 60°, to each end of the base, with the short
ENGINEER AND MACHINIST’S DRAWING-BOOK.
pose, the triangle of 60° is preferable to that of 45°, as it
is longer and lighter.
When the parallels and perpendiculars do not coincide
in direction with the edges of the board, the square may
be adjusted with its bevel stock to the obliquity required,
and the lines may be drawn as before. This is probably
the best plan when the oblique lines are numerous or
extensive. In most cases, however, oblique lines are only
occasional, and when their position is given they may be
drawn with a straight-edge. When the oblique parallels
and perpendiculars are short, as in oblique framing, short
rods, or bars, bolt-heads, and the like, the combined use of
the straight-edge and triangle is expedient. Thus, to draw
a perpendicular to the oblique line A B (Fig. 118), at the
point C, set the straight-
edge and set-square in
conjunction, to bring
the long edge of the
square to coincide with
the given line at a b;
then shift the square
into the position show-
ing in dotting, while the straight-edge is held fast,
and draw the perpendicular. When a number of short
parallels are to be drawn to an oblique line A B (Fig. 119),
through given points C, D, E, set the triangle and
straight-edge as before, with the side a b coincident with
the given line; then slide the triangle into the positions
shown in dotting, to set the edge upon the given points,
and draw the parallels as required. The straight-edge, in
these cases, is oblique to the given line, and may in some
cases be inconveniently placed, requiring re-adjustment,
when a number of lines are to be drawn. It is thus some-
times convenient to employ a supplementary triangle ; in
the second case, for example, the triangle might be set to
the given line, slid down to the position E, and fixed
there ; and a second triangle placed on its edge E, which
would form a sliding surface parallel to the given line,
from which perpendiculars might be drawn. Or, the tri-
angle a b c (Fig. 120) may be placed with its edge a c to
coincide with the given line, and the straight-edge applied
to the side b c; sliding the triangle into the position a' b' c,
the edge a'd now forms a base-line parallel to the given
line from which perpendiculars may be drawn with a
second triangle d.
Parallel rulers are also frequently used for drawing
oblique lines. We have no great opinion of them, except
for sketching jobs, as they are at best inconvenient for
working, and liable to derangement at the joints.
It remains to consider the utility of the sector in draw-
ing oblique parallel lines. This instrument should be stiff
enough at the joint not to yield too readily; and by set-
ting it to the obliquity required, it may be slid along the
square-blade, and may thus command the entire range of
the board. By sliding the triangle upon the sector, oblique
perpendiculars may also be drawn, as in (Fig. 118).
Frequently, short oblique lines, perpendicular to each
other, require to be drawn at the same place; this may
occasionally be done in one setting of the sector or straight-
edge, by placing the slant side of the triangle next it, and
exposing the right angle.
Thus, in drawing a
square nut n (Fig. 121), it
is plain from the figure,
that by presenting the
two edges of the tri-
angle successively, all
the sides of the nut may be drawn.
Square figures may be quickly described with the use
of the board. If they are to be described on a given
centre, C (Fig. 122), describe a circle with the radius C D
equal to half the side of the square, draw parallels A B,
E F, with the square, touching the top and bottom of the
circle, which may be very correctly drawn as tangents by
the eye, and with the set-square draw the upright tan-
gents, in the manner shown in dotting, to complete the
figure.
(.Fig. 122.) (Fig. 123.)
If the square is to be drawn upon a given line A B
(Fig. 123), draw the diagonal lines A F, BE, from the ends
of the line, by means of the set-square of 45°, as exempli-
fied in the figure, and draw perpendiculars from the same
points, cutting the diagonals at E, F ; join E F to com-
plete the figure.
To draw an octagon, apply the set-square of 45° to the
corners, after completing a square figure, and draw tan-
gents to the inscribed circle, as, for example, the line h k,
(Fig. 114).
To draw an equilateral triangle upon a given line A B
(Fig. 124), it is only necessary to apply the slant edge of the
set-square of 60°, to each end of the base, with the short